Properties

Label 400.6.c.j.49.2
Level $400$
Weight $6$
Character 400.49
Analytic conductor $64.154$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 400.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(64.1535279252\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 400.49
Dual form 400.6.c.j.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000i q^{3} +192.000i q^{7} +227.000 q^{9} +O(q^{10})\) \(q+4.00000i q^{3} +192.000i q^{7} +227.000 q^{9} +148.000 q^{11} +286.000i q^{13} +1678.00i q^{17} +1060.00 q^{19} -768.000 q^{21} -2976.00i q^{23} +1880.00i q^{27} +3410.00 q^{29} +2448.00 q^{31} +592.000i q^{33} -182.000i q^{37} -1144.00 q^{39} -9398.00 q^{41} +1244.00i q^{43} -12088.0i q^{47} -20057.0 q^{49} -6712.00 q^{51} +23846.0i q^{53} +4240.00i q^{57} -20020.0 q^{59} +32302.0 q^{61} +43584.0i q^{63} +60972.0i q^{67} +11904.0 q^{69} +32648.0 q^{71} -38774.0i q^{73} +28416.0i q^{77} -33360.0 q^{79} +47641.0 q^{81} -16716.0i q^{83} +13640.0i q^{87} -101370. q^{89} -54912.0 q^{91} +9792.00i q^{93} +119038. i q^{97} +33596.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 454 q^{9} + O(q^{10}) \) \( 2 q + 454 q^{9} + 296 q^{11} + 2120 q^{19} - 1536 q^{21} + 6820 q^{29} + 4896 q^{31} - 2288 q^{39} - 18796 q^{41} - 40114 q^{49} - 13424 q^{51} - 40040 q^{59} + 64604 q^{61} + 23808 q^{69} + 65296 q^{71} - 66720 q^{79} + 95282 q^{81} - 202740 q^{89} - 109824 q^{91} + 67192 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.00000i 0.256600i 0.991735 + 0.128300i \(0.0409521\pi\)
−0.991735 + 0.128300i \(0.959048\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 192.000i 1.48100i 0.672054 + 0.740502i \(0.265412\pi\)
−0.672054 + 0.740502i \(0.734588\pi\)
\(8\) 0 0
\(9\) 227.000 0.934156
\(10\) 0 0
\(11\) 148.000 0.368791 0.184395 0.982852i \(-0.440967\pi\)
0.184395 + 0.982852i \(0.440967\pi\)
\(12\) 0 0
\(13\) 286.000i 0.469362i 0.972072 + 0.234681i \(0.0754045\pi\)
−0.972072 + 0.234681i \(0.924595\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1678.00i 1.40822i 0.710092 + 0.704109i \(0.248653\pi\)
−0.710092 + 0.704109i \(0.751347\pi\)
\(18\) 0 0
\(19\) 1060.00 0.673631 0.336815 0.941571i \(-0.390650\pi\)
0.336815 + 0.941571i \(0.390650\pi\)
\(20\) 0 0
\(21\) −768.000 −0.380026
\(22\) 0 0
\(23\) − 2976.00i − 1.17304i −0.809934 0.586521i \(-0.800497\pi\)
0.809934 0.586521i \(-0.199503\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1880.00i 0.496305i
\(28\) 0 0
\(29\) 3410.00 0.752938 0.376469 0.926429i \(-0.377138\pi\)
0.376469 + 0.926429i \(0.377138\pi\)
\(30\) 0 0
\(31\) 2448.00 0.457517 0.228758 0.973483i \(-0.426533\pi\)
0.228758 + 0.973483i \(0.426533\pi\)
\(32\) 0 0
\(33\) 592.000i 0.0946317i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 182.000i − 0.0218558i −0.999940 0.0109279i \(-0.996521\pi\)
0.999940 0.0109279i \(-0.00347853\pi\)
\(38\) 0 0
\(39\) −1144.00 −0.120438
\(40\) 0 0
\(41\) −9398.00 −0.873124 −0.436562 0.899674i \(-0.643804\pi\)
−0.436562 + 0.899674i \(0.643804\pi\)
\(42\) 0 0
\(43\) 1244.00i 0.102600i 0.998683 + 0.0513002i \(0.0163365\pi\)
−0.998683 + 0.0513002i \(0.983663\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 12088.0i − 0.798196i −0.916908 0.399098i \(-0.869323\pi\)
0.916908 0.399098i \(-0.130677\pi\)
\(48\) 0 0
\(49\) −20057.0 −1.19337
\(50\) 0 0
\(51\) −6712.00 −0.361349
\(52\) 0 0
\(53\) 23846.0i 1.16607i 0.812446 + 0.583037i \(0.198136\pi\)
−0.812446 + 0.583037i \(0.801864\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4240.00i 0.172854i
\(58\) 0 0
\(59\) −20020.0 −0.748745 −0.374373 0.927278i \(-0.622142\pi\)
−0.374373 + 0.927278i \(0.622142\pi\)
\(60\) 0 0
\(61\) 32302.0 1.11149 0.555744 0.831353i \(-0.312433\pi\)
0.555744 + 0.831353i \(0.312433\pi\)
\(62\) 0 0
\(63\) 43584.0i 1.38349i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 60972.0i 1.65937i 0.558231 + 0.829685i \(0.311480\pi\)
−0.558231 + 0.829685i \(0.688520\pi\)
\(68\) 0 0
\(69\) 11904.0 0.301003
\(70\) 0 0
\(71\) 32648.0 0.768618 0.384309 0.923204i \(-0.374440\pi\)
0.384309 + 0.923204i \(0.374440\pi\)
\(72\) 0 0
\(73\) − 38774.0i − 0.851596i −0.904818 0.425798i \(-0.859993\pi\)
0.904818 0.425798i \(-0.140007\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 28416.0i 0.546180i
\(78\) 0 0
\(79\) −33360.0 −0.601393 −0.300696 0.953720i \(-0.597219\pi\)
−0.300696 + 0.953720i \(0.597219\pi\)
\(80\) 0 0
\(81\) 47641.0 0.806805
\(82\) 0 0
\(83\) − 16716.0i − 0.266340i −0.991093 0.133170i \(-0.957484\pi\)
0.991093 0.133170i \(-0.0425157\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 13640.0i 0.193204i
\(88\) 0 0
\(89\) −101370. −1.35655 −0.678273 0.734810i \(-0.737271\pi\)
−0.678273 + 0.734810i \(0.737271\pi\)
\(90\) 0 0
\(91\) −54912.0 −0.695126
\(92\) 0 0
\(93\) 9792.00i 0.117399i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 119038.i 1.28457i 0.766468 + 0.642283i \(0.222013\pi\)
−0.766468 + 0.642283i \(0.777987\pi\)
\(98\) 0 0
\(99\) 33596.0 0.344508
\(100\) 0 0
\(101\) −89898.0 −0.876893 −0.438446 0.898757i \(-0.644471\pi\)
−0.438446 + 0.898757i \(0.644471\pi\)
\(102\) 0 0
\(103\) 19504.0i 0.181147i 0.995890 + 0.0905734i \(0.0288700\pi\)
−0.995890 + 0.0905734i \(0.971130\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 158292.i 1.33659i 0.743895 + 0.668297i \(0.232976\pi\)
−0.743895 + 0.668297i \(0.767024\pi\)
\(108\) 0 0
\(109\) −36830.0 −0.296917 −0.148459 0.988919i \(-0.547431\pi\)
−0.148459 + 0.988919i \(0.547431\pi\)
\(110\) 0 0
\(111\) 728.000 0.00560821
\(112\) 0 0
\(113\) 11186.0i 0.0824098i 0.999151 + 0.0412049i \(0.0131196\pi\)
−0.999151 + 0.0412049i \(0.986880\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 64922.0i 0.438457i
\(118\) 0 0
\(119\) −322176. −2.08557
\(120\) 0 0
\(121\) −139147. −0.863993
\(122\) 0 0
\(123\) − 37592.0i − 0.224044i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 70552.0i 0.388150i 0.980987 + 0.194075i \(0.0621706\pi\)
−0.980987 + 0.194075i \(0.937829\pi\)
\(128\) 0 0
\(129\) −4976.00 −0.0263273
\(130\) 0 0
\(131\) −76452.0 −0.389234 −0.194617 0.980879i \(-0.562346\pi\)
−0.194617 + 0.980879i \(0.562346\pi\)
\(132\) 0 0
\(133\) 203520.i 0.997650i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 144918.i 0.659661i 0.944040 + 0.329831i \(0.106992\pi\)
−0.944040 + 0.329831i \(0.893008\pi\)
\(138\) 0 0
\(139\) 112220. 0.492644 0.246322 0.969188i \(-0.420778\pi\)
0.246322 + 0.969188i \(0.420778\pi\)
\(140\) 0 0
\(141\) 48352.0 0.204817
\(142\) 0 0
\(143\) 42328.0i 0.173096i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 80228.0i − 0.306219i
\(148\) 0 0
\(149\) −403750. −1.48986 −0.744932 0.667140i \(-0.767518\pi\)
−0.744932 + 0.667140i \(0.767518\pi\)
\(150\) 0 0
\(151\) 446648. 1.59413 0.797064 0.603895i \(-0.206385\pi\)
0.797064 + 0.603895i \(0.206385\pi\)
\(152\) 0 0
\(153\) 380906.i 1.31550i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 262258.i 0.849141i 0.905395 + 0.424570i \(0.139575\pi\)
−0.905395 + 0.424570i \(0.860425\pi\)
\(158\) 0 0
\(159\) −95384.0 −0.299215
\(160\) 0 0
\(161\) 571392. 1.73728
\(162\) 0 0
\(163\) 154564.i 0.455658i 0.973701 + 0.227829i \(0.0731628\pi\)
−0.973701 + 0.227829i \(0.926837\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 396672.i 1.10063i 0.834958 + 0.550314i \(0.185492\pi\)
−0.834958 + 0.550314i \(0.814508\pi\)
\(168\) 0 0
\(169\) 289497. 0.779700
\(170\) 0 0
\(171\) 240620. 0.629276
\(172\) 0 0
\(173\) − 573474.i − 1.45680i −0.685155 0.728398i \(-0.740265\pi\)
0.685155 0.728398i \(-0.259735\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) − 80080.0i − 0.192128i
\(178\) 0 0
\(179\) −594460. −1.38672 −0.693362 0.720589i \(-0.743871\pi\)
−0.693362 + 0.720589i \(0.743871\pi\)
\(180\) 0 0
\(181\) −107098. −0.242988 −0.121494 0.992592i \(-0.538769\pi\)
−0.121494 + 0.992592i \(0.538769\pi\)
\(182\) 0 0
\(183\) 129208.i 0.285208i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 248344.i 0.519337i
\(188\) 0 0
\(189\) −360960. −0.735029
\(190\) 0 0
\(191\) −469552. −0.931323 −0.465661 0.884963i \(-0.654184\pi\)
−0.465661 + 0.884963i \(0.654184\pi\)
\(192\) 0 0
\(193\) 52706.0i 0.101851i 0.998702 + 0.0509257i \(0.0162172\pi\)
−0.998702 + 0.0509257i \(0.983783\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 455862.i − 0.836889i −0.908242 0.418444i \(-0.862575\pi\)
0.908242 0.418444i \(-0.137425\pi\)
\(198\) 0 0
\(199\) 865000. 1.54840 0.774200 0.632940i \(-0.218152\pi\)
0.774200 + 0.632940i \(0.218152\pi\)
\(200\) 0 0
\(201\) −243888. −0.425795
\(202\) 0 0
\(203\) 654720.i 1.11510i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 675552.i − 1.09580i
\(208\) 0 0
\(209\) 156880. 0.248429
\(210\) 0 0
\(211\) −1.10565e6 −1.70967 −0.854835 0.518900i \(-0.826342\pi\)
−0.854835 + 0.518900i \(0.826342\pi\)
\(212\) 0 0
\(213\) 130592.i 0.197228i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 470016.i 0.677584i
\(218\) 0 0
\(219\) 155096. 0.218520
\(220\) 0 0
\(221\) −479908. −0.660963
\(222\) 0 0
\(223\) − 1.12158e6i − 1.51031i −0.655545 0.755156i \(-0.727561\pi\)
0.655545 0.755156i \(-0.272439\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 23348.0i − 0.0300736i −0.999887 0.0150368i \(-0.995213\pi\)
0.999887 0.0150368i \(-0.00478654\pi\)
\(228\) 0 0
\(229\) 596010. 0.751043 0.375522 0.926814i \(-0.377464\pi\)
0.375522 + 0.926814i \(0.377464\pi\)
\(230\) 0 0
\(231\) −113664. −0.140150
\(232\) 0 0
\(233\) − 485334.i − 0.585667i −0.956163 0.292834i \(-0.905402\pi\)
0.956163 0.292834i \(-0.0945982\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) − 133440.i − 0.154317i
\(238\) 0 0
\(239\) −48880.0 −0.0553524 −0.0276762 0.999617i \(-0.508811\pi\)
−0.0276762 + 0.999617i \(0.508811\pi\)
\(240\) 0 0
\(241\) −110798. −0.122882 −0.0614411 0.998111i \(-0.519570\pi\)
−0.0614411 + 0.998111i \(0.519570\pi\)
\(242\) 0 0
\(243\) 647404.i 0.703331i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 303160.i 0.316176i
\(248\) 0 0
\(249\) 66864.0 0.0683430
\(250\) 0 0
\(251\) 1.64375e6 1.64684 0.823419 0.567434i \(-0.192064\pi\)
0.823419 + 0.567434i \(0.192064\pi\)
\(252\) 0 0
\(253\) − 440448.i − 0.432607i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 1.30624e6i − 1.23365i −0.787102 0.616823i \(-0.788419\pi\)
0.787102 0.616823i \(-0.211581\pi\)
\(258\) 0 0
\(259\) 34944.0 0.0323685
\(260\) 0 0
\(261\) 774070. 0.703362
\(262\) 0 0
\(263\) − 2.12834e6i − 1.89736i −0.316231 0.948682i \(-0.602417\pi\)
0.316231 0.948682i \(-0.397583\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 405480.i − 0.348090i
\(268\) 0 0
\(269\) 1.44109e6 1.21426 0.607128 0.794604i \(-0.292321\pi\)
0.607128 + 0.794604i \(0.292321\pi\)
\(270\) 0 0
\(271\) 93248.0 0.0771288 0.0385644 0.999256i \(-0.487722\pi\)
0.0385644 + 0.999256i \(0.487722\pi\)
\(272\) 0 0
\(273\) − 219648.i − 0.178370i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 110298.i 0.0863711i 0.999067 + 0.0431855i \(0.0137507\pi\)
−0.999067 + 0.0431855i \(0.986249\pi\)
\(278\) 0 0
\(279\) 555696. 0.427392
\(280\) 0 0
\(281\) −192198. −0.145205 −0.0726027 0.997361i \(-0.523131\pi\)
−0.0726027 + 0.997361i \(0.523131\pi\)
\(282\) 0 0
\(283\) 331884.i 0.246332i 0.992386 + 0.123166i \(0.0393047\pi\)
−0.992386 + 0.123166i \(0.960695\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 1.80442e6i − 1.29310i
\(288\) 0 0
\(289\) −1.39583e6 −0.983076
\(290\) 0 0
\(291\) −476152. −0.329620
\(292\) 0 0
\(293\) 2.19481e6i 1.49358i 0.665063 + 0.746788i \(0.268405\pi\)
−0.665063 + 0.746788i \(0.731595\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 278240.i 0.183033i
\(298\) 0 0
\(299\) 851136. 0.550581
\(300\) 0 0
\(301\) −238848. −0.151952
\(302\) 0 0
\(303\) − 359592.i − 0.225011i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 2.37751e6i − 1.43971i −0.694123 0.719857i \(-0.744207\pi\)
0.694123 0.719857i \(-0.255793\pi\)
\(308\) 0 0
\(309\) −78016.0 −0.0464823
\(310\) 0 0
\(311\) 2.37305e6 1.39125 0.695626 0.718405i \(-0.255127\pi\)
0.695626 + 0.718405i \(0.255127\pi\)
\(312\) 0 0
\(313\) − 1.42941e6i − 0.824702i −0.911025 0.412351i \(-0.864708\pi\)
0.911025 0.412351i \(-0.135292\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 2.12462e6i − 1.18750i −0.804650 0.593750i \(-0.797647\pi\)
0.804650 0.593750i \(-0.202353\pi\)
\(318\) 0 0
\(319\) 504680. 0.277677
\(320\) 0 0
\(321\) −633168. −0.342970
\(322\) 0 0
\(323\) 1.77868e6i 0.948618i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 147320.i − 0.0761890i
\(328\) 0 0
\(329\) 2.32090e6 1.18213
\(330\) 0 0
\(331\) −3.09985e6 −1.55515 −0.777573 0.628793i \(-0.783549\pi\)
−0.777573 + 0.628793i \(0.783549\pi\)
\(332\) 0 0
\(333\) − 41314.0i − 0.0204168i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 2.40008e6i − 1.15120i −0.817731 0.575601i \(-0.804768\pi\)
0.817731 0.575601i \(-0.195232\pi\)
\(338\) 0 0
\(339\) −44744.0 −0.0211464
\(340\) 0 0
\(341\) 362304. 0.168728
\(342\) 0 0
\(343\) − 624000.i − 0.286384i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.77741e6i 0.792436i 0.918156 + 0.396218i \(0.129678\pi\)
−0.918156 + 0.396218i \(0.870322\pi\)
\(348\) 0 0
\(349\) 2.14805e6 0.944019 0.472010 0.881593i \(-0.343529\pi\)
0.472010 + 0.881593i \(0.343529\pi\)
\(350\) 0 0
\(351\) −537680. −0.232946
\(352\) 0 0
\(353\) − 661854.i − 0.282700i −0.989960 0.141350i \(-0.954856\pi\)
0.989960 0.141350i \(-0.0451443\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) − 1.28870e6i − 0.535159i
\(358\) 0 0
\(359\) −259320. −0.106194 −0.0530970 0.998589i \(-0.516909\pi\)
−0.0530970 + 0.998589i \(0.516909\pi\)
\(360\) 0 0
\(361\) −1.35250e6 −0.546222
\(362\) 0 0
\(363\) − 556588.i − 0.221701i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 1.49993e6i − 0.581307i −0.956828 0.290653i \(-0.906127\pi\)
0.956828 0.290653i \(-0.0938726\pi\)
\(368\) 0 0
\(369\) −2.13335e6 −0.815634
\(370\) 0 0
\(371\) −4.57843e6 −1.72696
\(372\) 0 0
\(373\) − 2.23807e6i − 0.832918i −0.909154 0.416459i \(-0.863271\pi\)
0.909154 0.416459i \(-0.136729\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 975260.i 0.353400i
\(378\) 0 0
\(379\) 3.15934e6 1.12979 0.564896 0.825162i \(-0.308916\pi\)
0.564896 + 0.825162i \(0.308916\pi\)
\(380\) 0 0
\(381\) −282208. −0.0995994
\(382\) 0 0
\(383\) − 342216.i − 0.119207i −0.998222 0.0596037i \(-0.981016\pi\)
0.998222 0.0596037i \(-0.0189837\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 282388.i 0.0958449i
\(388\) 0 0
\(389\) −88470.0 −0.0296430 −0.0148215 0.999890i \(-0.504718\pi\)
−0.0148215 + 0.999890i \(0.504718\pi\)
\(390\) 0 0
\(391\) 4.99373e6 1.65190
\(392\) 0 0
\(393\) − 305808.i − 0.0998775i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.45674e6i 1.73763i 0.495138 + 0.868814i \(0.335117\pi\)
−0.495138 + 0.868814i \(0.664883\pi\)
\(398\) 0 0
\(399\) −814080. −0.255997
\(400\) 0 0
\(401\) 4.04680e6 1.25676 0.628378 0.777908i \(-0.283719\pi\)
0.628378 + 0.777908i \(0.283719\pi\)
\(402\) 0 0
\(403\) 700128.i 0.214741i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 26936.0i − 0.00806022i
\(408\) 0 0
\(409\) 2.71207e6 0.801664 0.400832 0.916151i \(-0.368721\pi\)
0.400832 + 0.916151i \(0.368721\pi\)
\(410\) 0 0
\(411\) −579672. −0.169269
\(412\) 0 0
\(413\) − 3.84384e6i − 1.10889i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 448880.i 0.126413i
\(418\) 0 0
\(419\) 3.71746e6 1.03445 0.517227 0.855848i \(-0.326964\pi\)
0.517227 + 0.855848i \(0.326964\pi\)
\(420\) 0 0
\(421\) 3.55250e6 0.976853 0.488426 0.872605i \(-0.337571\pi\)
0.488426 + 0.872605i \(0.337571\pi\)
\(422\) 0 0
\(423\) − 2.74398e6i − 0.745640i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.20198e6i 1.64612i
\(428\) 0 0
\(429\) −169312. −0.0444165
\(430\) 0 0
\(431\) 4.06205e6 1.05330 0.526650 0.850082i \(-0.323448\pi\)
0.526650 + 0.850082i \(0.323448\pi\)
\(432\) 0 0
\(433\) 7.26287e6i 1.86161i 0.365518 + 0.930804i \(0.380892\pi\)
−0.365518 + 0.930804i \(0.619108\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 3.15456e6i − 0.790197i
\(438\) 0 0
\(439\) −5.41028e6 −1.33986 −0.669928 0.742426i \(-0.733675\pi\)
−0.669928 + 0.742426i \(0.733675\pi\)
\(440\) 0 0
\(441\) −4.55294e6 −1.11480
\(442\) 0 0
\(443\) 6.51524e6i 1.57733i 0.614826 + 0.788663i \(0.289226\pi\)
−0.614826 + 0.788663i \(0.710774\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 1.61500e6i − 0.382299i
\(448\) 0 0
\(449\) 509950. 0.119375 0.0596873 0.998217i \(-0.480990\pi\)
0.0596873 + 0.998217i \(0.480990\pi\)
\(450\) 0 0
\(451\) −1.39090e6 −0.322000
\(452\) 0 0
\(453\) 1.78659e6i 0.409053i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 1.22084e6i − 0.273444i −0.990609 0.136722i \(-0.956343\pi\)
0.990609 0.136722i \(-0.0436568\pi\)
\(458\) 0 0
\(459\) −3.15464e6 −0.698905
\(460\) 0 0
\(461\) −4.07210e6 −0.892413 −0.446207 0.894930i \(-0.647225\pi\)
−0.446207 + 0.894930i \(0.647225\pi\)
\(462\) 0 0
\(463\) − 2.02294e6i − 0.438561i −0.975662 0.219280i \(-0.929629\pi\)
0.975662 0.219280i \(-0.0703709\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.25097e6i 0.689797i 0.938640 + 0.344898i \(0.112087\pi\)
−0.938640 + 0.344898i \(0.887913\pi\)
\(468\) 0 0
\(469\) −1.17066e7 −2.45753
\(470\) 0 0
\(471\) −1.04903e6 −0.217890
\(472\) 0 0
\(473\) 184112.i 0.0378381i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.41304e6i 1.08929i
\(478\) 0 0
\(479\) −3.27936e6 −0.653056 −0.326528 0.945188i \(-0.605879\pi\)
−0.326528 + 0.945188i \(0.605879\pi\)
\(480\) 0 0
\(481\) 52052.0 0.0102583
\(482\) 0 0
\(483\) 2.28557e6i 0.445786i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 8.53197e6i − 1.63015i −0.579357 0.815074i \(-0.696696\pi\)
0.579357 0.815074i \(-0.303304\pi\)
\(488\) 0 0
\(489\) −618256. −0.116922
\(490\) 0 0
\(491\) −1.51265e6 −0.283162 −0.141581 0.989927i \(-0.545219\pi\)
−0.141581 + 0.989927i \(0.545219\pi\)
\(492\) 0 0
\(493\) 5.72198e6i 1.06030i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.26842e6i 1.13833i
\(498\) 0 0
\(499\) −6.49190e6 −1.16713 −0.583567 0.812065i \(-0.698343\pi\)
−0.583567 + 0.812065i \(0.698343\pi\)
\(500\) 0 0
\(501\) −1.58669e6 −0.282421
\(502\) 0 0
\(503\) − 8.61770e6i − 1.51870i −0.650684 0.759349i \(-0.725518\pi\)
0.650684 0.759349i \(-0.274482\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.15799e6i 0.200071i
\(508\) 0 0
\(509\) −2.67323e6 −0.457343 −0.228671 0.973504i \(-0.573438\pi\)
−0.228671 + 0.973504i \(0.573438\pi\)
\(510\) 0 0
\(511\) 7.44461e6 1.26122
\(512\) 0 0
\(513\) 1.99280e6i 0.334326i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) − 1.78902e6i − 0.294367i
\(518\) 0 0
\(519\) 2.29390e6 0.373814
\(520\) 0 0
\(521\) 6.18500e6 0.998264 0.499132 0.866526i \(-0.333652\pi\)
0.499132 + 0.866526i \(0.333652\pi\)
\(522\) 0 0
\(523\) 6.89452e6i 1.10217i 0.834448 + 0.551087i \(0.185787\pi\)
−0.834448 + 0.551087i \(0.814213\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.10774e6i 0.644283i
\(528\) 0 0
\(529\) −2.42023e6 −0.376026
\(530\) 0 0
\(531\) −4.54454e6 −0.699445
\(532\) 0 0
\(533\) − 2.68783e6i − 0.409811i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) − 2.37784e6i − 0.355834i
\(538\) 0 0
\(539\) −2.96844e6 −0.440104
\(540\) 0 0
\(541\) 155502. 0.0228425 0.0114212 0.999935i \(-0.496364\pi\)
0.0114212 + 0.999935i \(0.496364\pi\)
\(542\) 0 0
\(543\) − 428392.i − 0.0623508i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.26544e7i 1.80831i 0.427201 + 0.904157i \(0.359500\pi\)
−0.427201 + 0.904157i \(0.640500\pi\)
\(548\) 0 0
\(549\) 7.33255e6 1.03830
\(550\) 0 0
\(551\) 3.61460e6 0.507202
\(552\) 0 0
\(553\) − 6.40512e6i − 0.890665i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.07786e6i 0.966638i 0.875444 + 0.483319i \(0.160569\pi\)
−0.875444 + 0.483319i \(0.839431\pi\)
\(558\) 0 0
\(559\) −355784. −0.0481567
\(560\) 0 0
\(561\) −993376. −0.133262
\(562\) 0 0
\(563\) − 846636.i − 0.112571i −0.998415 0.0562854i \(-0.982074\pi\)
0.998415 0.0562854i \(-0.0179257\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 9.14707e6i 1.19488i
\(568\) 0 0
\(569\) −4.96041e6 −0.642299 −0.321149 0.947029i \(-0.604069\pi\)
−0.321149 + 0.947029i \(0.604069\pi\)
\(570\) 0 0
\(571\) −8.96505e6 −1.15070 −0.575351 0.817907i \(-0.695134\pi\)
−0.575351 + 0.817907i \(0.695134\pi\)
\(572\) 0 0
\(573\) − 1.87821e6i − 0.238978i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.86080e6i 0.357724i 0.983874 + 0.178862i \(0.0572415\pi\)
−0.983874 + 0.178862i \(0.942758\pi\)
\(578\) 0 0
\(579\) −210824. −0.0261351
\(580\) 0 0
\(581\) 3.20947e6 0.394451
\(582\) 0 0
\(583\) 3.52921e6i 0.430037i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 6.74027e6i − 0.807387i −0.914894 0.403694i \(-0.867726\pi\)
0.914894 0.403694i \(-0.132274\pi\)
\(588\) 0 0
\(589\) 2.59488e6 0.308197
\(590\) 0 0
\(591\) 1.82345e6 0.214746
\(592\) 0 0
\(593\) − 1.78609e6i − 0.208578i −0.994547 0.104289i \(-0.966743\pi\)
0.994547 0.104289i \(-0.0332566\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3.46000e6i 0.397320i
\(598\) 0 0
\(599\) 4.94620e6 0.563254 0.281627 0.959524i \(-0.409126\pi\)
0.281627 + 0.959524i \(0.409126\pi\)
\(600\) 0 0
\(601\) −4.58100e6 −0.517337 −0.258669 0.965966i \(-0.583284\pi\)
−0.258669 + 0.965966i \(0.583284\pi\)
\(602\) 0 0
\(603\) 1.38406e7i 1.55011i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.07999e6i 0.779940i 0.920828 + 0.389970i \(0.127515\pi\)
−0.920828 + 0.389970i \(0.872485\pi\)
\(608\) 0 0
\(609\) −2.61888e6 −0.286136
\(610\) 0 0
\(611\) 3.45717e6 0.374643
\(612\) 0 0
\(613\) 5.09609e6i 0.547754i 0.961765 + 0.273877i \(0.0883061\pi\)
−0.961765 + 0.273877i \(0.911694\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.30003e7i 1.37480i 0.726279 + 0.687400i \(0.241248\pi\)
−0.726279 + 0.687400i \(0.758752\pi\)
\(618\) 0 0
\(619\) 4.84406e6 0.508139 0.254070 0.967186i \(-0.418231\pi\)
0.254070 + 0.967186i \(0.418231\pi\)
\(620\) 0 0
\(621\) 5.59488e6 0.582186
\(622\) 0 0
\(623\) − 1.94630e7i − 2.00905i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 627520.i 0.0637468i
\(628\) 0 0
\(629\) 305396. 0.0307777
\(630\) 0 0
\(631\) −6.22775e6 −0.622670 −0.311335 0.950300i \(-0.600776\pi\)
−0.311335 + 0.950300i \(0.600776\pi\)
\(632\) 0 0
\(633\) − 4.42261e6i − 0.438702i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 5.73630e6i − 0.560123i
\(638\) 0 0
\(639\) 7.41110e6 0.718010
\(640\) 0 0
\(641\) 1.53280e6 0.147347 0.0736734 0.997282i \(-0.476528\pi\)
0.0736734 + 0.997282i \(0.476528\pi\)
\(642\) 0 0
\(643\) 1.74382e7i 1.66332i 0.555287 + 0.831659i \(0.312609\pi\)
−0.555287 + 0.831659i \(0.687391\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 4.25469e6i − 0.399583i −0.979838 0.199792i \(-0.935974\pi\)
0.979838 0.199792i \(-0.0640265\pi\)
\(648\) 0 0
\(649\) −2.96296e6 −0.276130
\(650\) 0 0
\(651\) −1.88006e6 −0.173868
\(652\) 0 0
\(653\) 3.01085e6i 0.276316i 0.990410 + 0.138158i \(0.0441181\pi\)
−0.990410 + 0.138158i \(0.955882\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) − 8.80170e6i − 0.795524i
\(658\) 0 0
\(659\) −8.11462e6 −0.727871 −0.363936 0.931424i \(-0.618567\pi\)
−0.363936 + 0.931424i \(0.618567\pi\)
\(660\) 0 0
\(661\) 2.47370e6 0.220213 0.110107 0.993920i \(-0.464881\pi\)
0.110107 + 0.993920i \(0.464881\pi\)
\(662\) 0 0
\(663\) − 1.91963e6i − 0.169603i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 1.01482e7i − 0.883228i
\(668\) 0 0
\(669\) 4.48630e6 0.387546
\(670\) 0 0
\(671\) 4.78070e6 0.409907
\(672\) 0 0
\(673\) 5.77063e6i 0.491117i 0.969382 + 0.245559i \(0.0789714\pi\)
−0.969382 + 0.245559i \(0.921029\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 1.67197e7i − 1.40203i −0.713147 0.701014i \(-0.752731\pi\)
0.713147 0.701014i \(-0.247269\pi\)
\(678\) 0 0
\(679\) −2.28553e7 −1.90245
\(680\) 0 0
\(681\) 93392.0 0.00771688
\(682\) 0 0
\(683\) − 7.14532e6i − 0.586097i −0.956098 0.293049i \(-0.905330\pi\)
0.956098 0.293049i \(-0.0946698\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.38404e6i 0.192718i
\(688\) 0 0
\(689\) −6.81996e6 −0.547310
\(690\) 0 0
\(691\) 8.78395e6 0.699833 0.349917 0.936781i \(-0.386210\pi\)
0.349917 + 0.936781i \(0.386210\pi\)
\(692\) 0 0
\(693\) 6.45043e6i 0.510218i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) − 1.57698e7i − 1.22955i
\(698\) 0 0
\(699\) 1.94134e6 0.150282
\(700\) 0 0
\(701\) −1.60141e7 −1.23086 −0.615428 0.788193i \(-0.711017\pi\)
−0.615428 + 0.788193i \(0.711017\pi\)
\(702\) 0 0
\(703\) − 192920.i − 0.0147228i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 1.72604e7i − 1.29868i
\(708\) 0 0
\(709\) 1.91354e7 1.42962 0.714811 0.699318i \(-0.246513\pi\)
0.714811 + 0.699318i \(0.246513\pi\)
\(710\) 0 0
\(711\) −7.57272e6 −0.561795
\(712\) 0 0
\(713\) − 7.28525e6i − 0.536686i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) − 195520.i − 0.0142034i
\(718\) 0 0
\(719\) 1.02934e7 0.742566 0.371283 0.928520i \(-0.378918\pi\)
0.371283 + 0.928520i \(0.378918\pi\)
\(720\) 0 0
\(721\) −3.74477e6 −0.268279
\(722\) 0 0
\(723\) − 443192.i − 0.0315316i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 1.93264e7i − 1.35618i −0.734981 0.678088i \(-0.762809\pi\)
0.734981 0.678088i \(-0.237191\pi\)
\(728\) 0 0
\(729\) 8.98715e6 0.626330
\(730\) 0 0
\(731\) −2.08743e6 −0.144484
\(732\) 0 0
\(733\) 5.26197e6i 0.361733i 0.983508 + 0.180866i \(0.0578902\pi\)
−0.983508 + 0.180866i \(0.942110\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.02386e6i 0.611961i
\(738\) 0 0
\(739\) 2.82944e7 1.90585 0.952927 0.303199i \(-0.0980548\pi\)
0.952927 + 0.303199i \(0.0980548\pi\)
\(740\) 0 0
\(741\) −1.21264e6 −0.0811309
\(742\) 0 0
\(743\) − 2.09863e7i − 1.39464i −0.716759 0.697321i \(-0.754375\pi\)
0.716759 0.697321i \(-0.245625\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) − 3.79453e6i − 0.248804i
\(748\) 0 0
\(749\) −3.03921e7 −1.97950
\(750\) 0 0
\(751\) 1.89668e7 1.22714 0.613572 0.789639i \(-0.289732\pi\)
0.613572 + 0.789639i \(0.289732\pi\)
\(752\) 0 0
\(753\) 6.57499e6i 0.422579i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.08257e7i 0.686617i 0.939223 + 0.343309i \(0.111548\pi\)
−0.939223 + 0.343309i \(0.888452\pi\)
\(758\) 0 0
\(759\) 1.76179e6 0.111007
\(760\) 0 0
\(761\) 1.90534e7 1.19264 0.596322 0.802745i \(-0.296628\pi\)
0.596322 + 0.802745i \(0.296628\pi\)
\(762\) 0 0
\(763\) − 7.07136e6i − 0.439736i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 5.72572e6i − 0.351432i
\(768\) 0 0
\(769\) 1.57826e7 0.962415 0.481208 0.876607i \(-0.340198\pi\)
0.481208 + 0.876607i \(0.340198\pi\)
\(770\) 0 0
\(771\) 5.22497e6 0.316554
\(772\) 0 0
\(773\) − 2.44049e7i − 1.46902i −0.678598 0.734510i \(-0.737412\pi\)
0.678598 0.734510i \(-0.262588\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 139776.i 0.00830577i
\(778\) 0 0
\(779\) −9.96188e6 −0.588163
\(780\) 0 0
\(781\) 4.83190e6 0.283459
\(782\) 0 0
\(783\) 6.41080e6i 0.373687i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 3.37607e7i 1.94301i 0.237019 + 0.971505i \(0.423830\pi\)
−0.237019 + 0.971505i \(0.576170\pi\)
\(788\) 0 0
\(789\) 8.51334e6 0.486864
\(790\) 0 0
\(791\) −2.14771e6 −0.122049
\(792\) 0 0
\(793\) 9.23837e6i 0.521690i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 2.19885e7i − 1.22617i −0.790019 0.613083i \(-0.789929\pi\)
0.790019 0.613083i \(-0.210071\pi\)
\(798\) 0 0
\(799\) 2.02837e7 1.12403
\(800\) 0 0
\(801\) −2.30110e7 −1.26723
\(802\) 0 0
\(803\) − 5.73855e6i − 0.314061i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 5.76436e6i 0.311578i
\(808\) 0 0
\(809\) 2.93597e7 1.57717 0.788587 0.614923i \(-0.210813\pi\)
0.788587 + 0.614923i \(0.210813\pi\)
\(810\) 0 0
\(811\) −3.17703e7 −1.69617 −0.848083 0.529863i \(-0.822243\pi\)
−0.848083 + 0.529863i \(0.822243\pi\)
\(812\) 0 0
\(813\) 372992.i 0.0197912i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.31864e6i 0.0691148i
\(818\) 0 0
\(819\) −1.24650e7 −0.649357
\(820\) 0 0
\(821\) −2.71430e6 −0.140540 −0.0702699 0.997528i \(-0.522386\pi\)
−0.0702699 + 0.997528i \(0.522386\pi\)
\(822\) 0 0
\(823\) 1.25866e7i 0.647753i 0.946099 + 0.323877i \(0.104986\pi\)
−0.946099 + 0.323877i \(0.895014\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 8.72355e6i − 0.443537i −0.975099 0.221768i \(-0.928817\pi\)
0.975099 0.221768i \(-0.0711828\pi\)
\(828\) 0 0
\(829\) 1.06178e7 0.536597 0.268299 0.963336i \(-0.413539\pi\)
0.268299 + 0.963336i \(0.413539\pi\)
\(830\) 0 0
\(831\) −441192. −0.0221628
\(832\) 0 0
\(833\) − 3.36556e7i − 1.68053i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 4.60224e6i 0.227068i
\(838\) 0 0
\(839\) 1.67765e7 0.822805 0.411403 0.911454i \(-0.365039\pi\)
0.411403 + 0.911454i \(0.365039\pi\)
\(840\) 0 0
\(841\) −8.88305e6 −0.433084
\(842\) 0 0
\(843\) − 768792.i − 0.0372597i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 2.67162e7i − 1.27958i
\(848\) 0 0
\(849\) −1.32754e6 −0.0632087
\(850\) 0 0
\(851\) −541632. −0.0256378
\(852\) 0 0
\(853\) − 2.20186e7i − 1.03613i −0.855340 0.518067i \(-0.826652\pi\)
0.855340 0.518067i \(-0.173348\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 3.16676e7i − 1.47287i −0.676510 0.736434i \(-0.736508\pi\)
0.676510 0.736434i \(-0.263492\pi\)
\(858\) 0 0
\(859\) 1.58064e7 0.730886 0.365443 0.930834i \(-0.380918\pi\)
0.365443 + 0.930834i \(0.380918\pi\)
\(860\) 0 0
\(861\) 7.21766e6 0.331809
\(862\) 0 0
\(863\) 1.44287e7i 0.659476i 0.944072 + 0.329738i \(0.106960\pi\)
−0.944072 + 0.329738i \(0.893040\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 5.58331e6i − 0.252257i
\(868\) 0 0
\(869\) −4.93728e6 −0.221788
\(870\) 0 0
\(871\) −1.74380e7 −0.778845
\(872\) 0 0
\(873\) 2.70216e7i 1.19999i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 247902.i − 0.0108838i −0.999985 0.00544191i \(-0.998268\pi\)
0.999985 0.00544191i \(-0.00173222\pi\)
\(878\) 0 0
\(879\) −8.77922e6 −0.383252
\(880\) 0 0
\(881\) 4.10268e7 1.78085 0.890426 0.455128i \(-0.150406\pi\)
0.890426 + 0.455128i \(0.150406\pi\)
\(882\) 0 0
\(883\) − 4.18015e7i − 1.80422i −0.431503 0.902112i \(-0.642016\pi\)
0.431503 0.902112i \(-0.357984\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 2.10476e7i − 0.898241i −0.893471 0.449120i \(-0.851737\pi\)
0.893471 0.449120i \(-0.148263\pi\)
\(888\) 0 0
\(889\) −1.35460e7 −0.574852
\(890\) 0 0
\(891\) 7.05087e6 0.297542
\(892\) 0 0
\(893\) − 1.28133e7i − 0.537690i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 3.40454e6i 0.141279i
\(898\) 0 0
\(899\) 8.34768e6 0.344482
\(900\) 0 0
\(901\) −4.00136e7 −1.64208
\(902\) 0 0
\(903\) − 955392.i − 0.0389908i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 7.48309e6i 0.302039i 0.988531 + 0.151019i \(0.0482556\pi\)
−0.988531 + 0.151019i \(0.951744\pi\)
\(908\) 0 0
\(909\) −2.04068e7 −0.819155
\(910\) 0 0
\(911\) 6.63165e6 0.264744 0.132372 0.991200i \(-0.457741\pi\)
0.132372 + 0.991200i \(0.457741\pi\)
\(912\) 0 0
\(913\) − 2.47397e6i − 0.0982239i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 1.46788e7i − 0.576457i
\(918\) 0 0
\(919\) −1.68976e7 −0.659990 −0.329995 0.943983i \(-0.607047\pi\)
−0.329995 + 0.943983i \(0.607047\pi\)
\(920\) 0 0
\(921\) 9.51003e6 0.369431
\(922\) 0 0
\(923\) 9.33733e6i 0.360760i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 4.42741e6i 0.169219i
\(928\) 0 0
\(929\) 1.28653e7 0.489081 0.244541 0.969639i \(-0.421363\pi\)
0.244541 + 0.969639i \(0.421363\pi\)
\(930\) 0 0
\(931\) −2.12604e7 −0.803892
\(932\) 0 0
\(933\) 9.49219e6i 0.356995i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 1.06887e7i − 0.397718i −0.980028 0.198859i \(-0.936276\pi\)
0.980028 0.198859i \(-0.0637236\pi\)
\(938\) 0 0
\(939\) 5.71766e6 0.211619
\(940\) 0 0
\(941\) 2.82455e7 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(942\) 0 0
\(943\) 2.79684e7i 1.02421i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 1.70892e7i − 0.619222i −0.950863 0.309611i \(-0.899801\pi\)
0.950863 0.309611i \(-0.100199\pi\)
\(948\) 0 0
\(949\) 1.10894e7 0.399706
\(950\) 0 0
\(951\) 8.49849e6 0.304713
\(952\) 0 0
\(953\) 2.22259e7i 0.792735i 0.918092 + 0.396367i \(0.129729\pi\)
−0.918092 + 0.396367i \(0.870271\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 2.01872e6i 0.0712519i
\(958\) 0 0
\(959\) −2.78243e7 −0.976961
\(960\) 0 0
\(961\) −2.26364e7 −0.790678
\(962\) 0 0
\(963\) 3.59323e7i 1.24859i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 2.41551e7i 0.830696i 0.909663 + 0.415348i \(0.136340\pi\)
−0.909663 + 0.415348i \(0.863660\pi\)
\(968\) 0 0
\(969\) −7.11472e6 −0.243416
\(970\) 0 0
\(971\) 5.48313e7 1.86630 0.933149 0.359491i \(-0.117050\pi\)
0.933149 + 0.359491i \(0.117050\pi\)
\(972\) 0 0
\(973\) 2.15462e7i 0.729608i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.56612e7i 0.524915i 0.964944 + 0.262457i \(0.0845329\pi\)
−0.964944 + 0.262457i \(0.915467\pi\)
\(978\) 0 0
\(979\) −1.50028e7 −0.500281
\(980\) 0 0
\(981\) −8.36041e6 −0.277367
\(982\) 0 0
\(983\) 1.63420e7i 0.539412i 0.962943 + 0.269706i \(0.0869266\pi\)
−0.962943 + 0.269706i \(0.913073\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 9.28358e6i 0.303335i
\(988\) 0 0
\(989\) 3.70214e6 0.120355
\(990\) 0 0
\(991\) −1.37576e7 −0.444997 −0.222498 0.974933i \(-0.571421\pi\)
−0.222498 + 0.974933i \(0.571421\pi\)
\(992\) 0 0
\(993\) − 1.23994e7i − 0.399050i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.29097e7i 0.411320i 0.978624 + 0.205660i \(0.0659341\pi\)
−0.978624 + 0.205660i \(0.934066\pi\)
\(998\) 0 0
\(999\) 342160. 0.0108471
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 400.6.c.j.49.2 2
4.3 odd 2 25.6.b.a.24.1 2
5.2 odd 4 80.6.a.e.1.1 1
5.3 odd 4 400.6.a.g.1.1 1
5.4 even 2 inner 400.6.c.j.49.1 2
12.11 even 2 225.6.b.e.199.2 2
15.2 even 4 720.6.a.a.1.1 1
20.3 even 4 25.6.a.a.1.1 1
20.7 even 4 5.6.a.a.1.1 1
20.19 odd 2 25.6.b.a.24.2 2
40.27 even 4 320.6.a.j.1.1 1
40.37 odd 4 320.6.a.g.1.1 1
60.23 odd 4 225.6.a.f.1.1 1
60.47 odd 4 45.6.a.b.1.1 1
60.59 even 2 225.6.b.e.199.1 2
140.27 odd 4 245.6.a.b.1.1 1
220.87 odd 4 605.6.a.a.1.1 1
260.207 even 4 845.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.6.a.a.1.1 1 20.7 even 4
25.6.a.a.1.1 1 20.3 even 4
25.6.b.a.24.1 2 4.3 odd 2
25.6.b.a.24.2 2 20.19 odd 2
45.6.a.b.1.1 1 60.47 odd 4
80.6.a.e.1.1 1 5.2 odd 4
225.6.a.f.1.1 1 60.23 odd 4
225.6.b.e.199.1 2 60.59 even 2
225.6.b.e.199.2 2 12.11 even 2
245.6.a.b.1.1 1 140.27 odd 4
320.6.a.g.1.1 1 40.37 odd 4
320.6.a.j.1.1 1 40.27 even 4
400.6.a.g.1.1 1 5.3 odd 4
400.6.c.j.49.1 2 5.4 even 2 inner
400.6.c.j.49.2 2 1.1 even 1 trivial
605.6.a.a.1.1 1 220.87 odd 4
720.6.a.a.1.1 1 15.2 even 4
845.6.a.b.1.1 1 260.207 even 4